arXiv subjects

Deewang Bhamidipati

Publications and source records attributed to Deewang Bhamidipati.

6 recordsLinked to original sources

arXiv2026

The Brauer Group of $\mathscr{Y}_0(2)$

We determine the Brauer group of the Deligne-Mumford stack $\mathscr{Y}_0(2)$, the moduli space of elliptic curves with a marked $2$-torsion subgroup over bases of arithmetic interest. Antieau and Meier determine the Brauer group for $\mathscr{M}_{1,1}$, the moduli stack of elliptic curves by exploiting the fact it is covered by the Legendre family and using the Hochschild-Serre spectral sequence. Over an algebraically closed field, Shin uses the coarse space map to determine the Brauer group of $\mathscr{M}_{1,1}$. We combine techniques from both papers to determine the Brauer group of $\mathscr{Y}_0(2)$.

math.AG↗

arXiv2026

On the classification of indecomposable Ekedahl-Oort strata in unitary Shimura varieties, and related Newton polygons

In this paper, we give a complete classification of indecomposable Ekedahl--Oort strata of Shimura varieties associated to the unitary group $\mathsf{GU}(a, b)$ over an odd inert prime. We show that each indecomposable stratum is one of four types: unitary unicycle, unitary bicycle, Serre unicycle, or Serre bicycle; the latter two types are named for a tensor construction of abelian varieties developed by Serre. We provide an algorithm that translates the description of a stratum in terms of words in the alphabet $\{\texttt{f},\texttt{v}\}$ to the corresponding Weyl group coset representative. Finally, using a $p$-adic lift, we construct a `tautological' point in each Ekedahl--Oort stratum, and compute its Newton polygon. As an application, we show that the indecomposable Ekedahl--Oort strata corresponding to unitary unicycles and Serre unicycles always intersect the supersingular locus.

math.NT↗

arXiv2025

Ekedahl-Oort strata in the $\mathsf{GU}(q-2,2)$ Shimura variety

This paper concerns the characteristic-$p$ fibers of $\mathsf{GU}(q-2,2)$ Shimura varieties, which classify abelian varieties with additional structure. These Shimura varieties admit two stratifications of interest: the Ekedahl-Oort stratification, based on the isomorphism class of the $p$-torsion subgroup scheme, and the Newton stratification, based on the isogeny class of the $p$-divisible group. In this paper, we present several novel techniques that give a better understanding of the Ekedahl-Oort stratification and of the interaction between the two stratifications for a general signature $(q-2,2)$.

math.NT↗

arXiv2025

The Ekedahl-Oort and Newton stratification of the $\mathsf{GU}(3,2)$ Shimura variety

This paper concerns the characteristic-$p$ fibers of $\mathsf{GU}(3,2)$ Shimura varieties. Such Shimura varieties parametrize abelian varieties in characteristic $p$ of dimension $5$ with an action of signature $(3,2)$ by an order in an imaginary quadratic field in which $p$ is inert. We completely describe the interaction of two stratifications of these Shimura varieties: the Ekedahl-Oort stratification, based on the isomorphism class of the $p$-torsion subgroup scheme, and the Newton stratification, based on the isogeny class of the $p$-divisible group. We identify which Ekedahl-Oort and Newton strata intersect.

math.NT↗

arXiv2025

Traverso's Isogeny Conjecture for Some Unitary p-Divisible Groups

The isogeny cutoff of a $p$-divisible group $X$ (defined over an algebraically closed field of characteristic $p$) measures the amount of $p$-torsion necessary to determine its isogeny class. The minimal height of $X$ measures its distance to the closest minimal $p$-divisible group (in the sense of Oort). In this paper, we study these invariants for supersingular unitary $p$-divisible groups of signature $(a,b)$. We provide a complete description of the possible minimal heights. As an application, we establish bounds on the isogeny cutoffs for these $p$-divisible groups. Finally, we rephrase our results in the language of the $\mathrm{BT}_m$ stratifications of unitary Shimura varieties of signature $(a,b)$.

math.NT↗

arXiv2024

Frobenius distributions of low dimensional abelian varieties over finite fields

Given a $g$-dimensional abelian variety $A$ over a finite field $\mathbf{F}_q$, the Weil conjectures imply that the normalized Frobenius eigenvalues generate a multiplicative group of rank at most $g$. The Pontryagin dual of this group is a compact abelian Lie group that controls the distribution of high powers of the Frobenius endomorphism. This group, which we call the Serre--Frobenius group, encodes the possible multiplicative relations between the Frobenius eigenvalues. In this article, we classify all possible Serre--Frobenius groups that occur for $g \le 3$. We also give a partial classification for simple ordinary abelian varieties of prime dimension $g>3$.

math.NT↗